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A051683 Triangle read by rows: a(n,k)=n!*k. 16
1, 2, 4, 6, 12, 18, 24, 48, 72, 96, 120, 240, 360, 480, 600, 720, 1440, 2160, 2880, 3600, 4320, 5040, 10080, 15120, 20160, 25200, 30240, 35280, 40320, 80640, 120960, 161280, 201600, 241920, 282240, 322560, 362880, 725760, 1088640, 1451520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers with only one nonzero digit when written in base factorial. - Franklin T. Adams-Watters, Nov 28 2011

In other words, numbers n such that A034968(n) = A099563(n). - Antti Karttunen, Jul 02 2013

LINKS

Reinhard Zumkeller, Rows n=1..150 of triangle, flattened

Tilman Piesk, Arrays of permutations

FORMULA

a(n) = A000142(A002024(n)) * A002260(n) = A002024(n)! * A002260(n). - Antti Karttunen, Jul 02 2013

EXAMPLE

Table begins

1

2 4

6 12 18

24 48 72 96 ...

MATHEMATICA

a[n_, k_] := n!*k; Flatten[Table[a[n, k], {n, 9}, {k, n}]] (* Jean-François Alcover, Apr 22 2011 *)

PROG

(Haskell)

a051683 n k = a051683_tabl !! (n-1) !! (k-1)

a051683_row n = a051683_tabl !! (n-1)

a051683_tabl = map fst $ iterate f ([1], 2) where

   f (row, n) = (row' ++ [head row' + last row'], n + 1) where

     row' = map (* n) row

-- Reinhard Zumkeller, Mar 09 2012

(Scheme): (define (A051683 n) (* (A000142 (A002024 n)) (A002260 n))) -- Antti Karttunen, Jul 02 2013

(MAGMA) [[Factorial(n)*k: k in [1..n]]: n in [1..15]]; // Vincenzo Librandi, Jun 15 2015

CROSSREFS

Cf. A000142, row sums give A001286(n+1).

Cf. A007623.

Cf. A200748.

Cf. A162608.

Sequence in context: A181416 A225566 A273009 * A215821 A192096 A181740

Adjacent sequences:  A051680 A051681 A051682 * A051684 A051685 A051686

KEYWORD

easy,nice,nonn,tabl

AUTHOR

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)

STATUS

approved

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Last modified December 10 09:41 EST 2016. Contains 278999 sequences.